EduSahara™ Worksheet

Question 1

1.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the distance between the point and the top of the
chimney
is
180 m
,
find the height of the
chimney
.

(i)

45

√

12

m
(ii)

180

m
(iii)

90

√

2

m
(iv)

90

m
(v)

180

√

3

m

Question 2

2.

Two vertical poles are on either side of a road. A 29 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.

(i)

44.61 m
(ii)

42.61 m
(iii)

39.61 m
(iv)

36.61 m
(v)

34.61 m

Question 3

3.

From a point 190 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the pillar.

(i)

211.39 m
(ii)

192.39 m
(iii)

237.39 m
(iv)

219.39 m
(v)

233.39 m

Question 4

4.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the flag staff is 16 m, find the height of the building .

(i)

24.85 m
(ii)

18.85 m
(iii)

21.85 m
(iv)

16.85 m
(v)

26.85 m

Question 5

5.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 60 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

245.93 m
(ii)

211.93 m
(iii)

208.93 m
(iv)

240.93 m
(v)

223.93 m

Question 6

6.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the height of the
tower
is
100 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

50

√

2

m
(ii)

100
3

√

3

m
(iii)

100

m
(iv)

100
3

m
(v)

100
3

√

18

m

Question 7

7.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
60°
.
If the distance between the point and the foot of the
building
is
120 m
,
find the height of the
building
.

(i)

180

√

2

m
(ii)

360

m
(iii)

120

√

18

m
(iv)

120

√

3

m
(v)

120

m

Question 8

8.

From the top of a light house which is 55 m high from the sea level, the angles of depression of two ships are 45° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

43.25 m
(ii)

35.25 m
(iii)

40.25 m
(iv)

45.25 m
(v)

37.25 m

Question 9

9.

Two boys are on opposite sides of a tower of 80 m height. They measure the angle of elevation of the top of the tower as 30° and 60° respectively. Find the distance between the two boys.

(i)

320
3

m
(ii)

320
3

√

18

m
(iii)

320
3

√

3

m
(iv)

320

m
(v)

160

√

2

m

Question 10

10.

The shadow of a vertical tower BA on a level ground is increased by 30 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .

(i)

73.98 m
(ii)

75.98 m
(iii)

70.98 m
(iv)

65.98 m
(v)

67.98 m

Question 11

11.

A man 1.5 m tall stands at a distance of 9.7 m from a lamp post and casts a shadow of 8.2 m on the ground. Find the height of the lamp post .

(i)

5.27 m
(ii)

2.27 m
(iii)

1.27 m
(iv)

4.27 m
(v)

3.27 m

Question 12

12.

A man in a boat rowing away from a lighthouse 75 m high, takes 4 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.

(i)

2.23 m/sec
(ii)

0.23 m/sec
(iii)

7.23 m/sec
(iv)

1.23 m/sec
(v)

8.23 m/sec

Question 13

13.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 50 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .

(i)

53.00 m
(ii)

50.00 m
(iii)

47.00 m
(iv)

45.00 m
(v)

55.00 m

Question 14

14.

From a point 200 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the cliff.

(i)

122.48 m
(ii)

140.48 m
(iii)

97.48 m
(iv)

99.48 m
(v)

115.48 m

Question 15

15.

A person, walking 10 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .

(i)

15
2

√

2

m
(ii)

15

m
(iii)

5

√

18

m
(iv)

5

m
(v)

5

√

3

m

Question 16

16.

The angles of depression of two boats from the top of a cliff 200 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

521.42 m
(ii)

546.42 m
(iii)

552.42 m
(iv)

560.42 m
(v)

538.42 m

Question 17

17.

The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 30°. If the height of the tower is 75 m, find the height of the building .

(i)

132.89 m
(ii)

129.89 m
(iii)

117.89 m
(iv)

145.89 m

Question 18

18.

From the top of a 13 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.

(i)

30.52 m
(ii)

40.52 m
(iii)

35.52 m
(iv)

32.52 m
(v)

38.52 m

Question 19

19.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 10 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?

(i)

12 min 39 sec
(ii)

16 min 42 sec
(iii)

11 min 38 sec
(iv)

14 min 41 sec
(v)

13 min 40 sec

Question 20

20.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 7 m, find the height of the flag staff .

(i)

9.00 m
(ii)

17.00 m
(iii)

19.00 m
(iv)

11.00 m
(v)

14.00 m

Question 21

21.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 45° and 60° and the distance between them is 125 m , find the height of the cliff.

(i)

76.25 m
(ii)

82.25 m
(iii)

74.25 m
(iv)

84.25 m
(v)

79.25 m

Question 22

22.

A
tower
stands vertically on the ground.

The height of the
tower
is
160

√

2

m
.

The distance between the observation point and its top
is
320

m
.

Find the angle of elevation.

(i)

105°
(ii)

75°
(iii)

60°
(iv)

45°
(v)

30°

Question 23

23.

A flagstaff stands on the top of a building at a distance of 20 m away from the foot of building . The angle of elevation of the top of the flagstaff is 45° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

(

20

√

6

−

20
3

√

18

)

m
(ii)

(

20

−

20
3

√

3

)

m
(iii)

800
3

m
(iv)

(

10

√

6

−

10

√

2

)

m
(v)

(

2

−

√

3

)

m

Question 24

24.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠d
(ii)

∠e
(iii)

∠g
(iv)

∠f

Question 25

25.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
45°
.
If the distance between the point and the foot of the
radio tower
is
10 m
,
find the distance between
the observation point and the top of the
radio tower
.

(i)

10

m
(ii)

20

√

3

m
(iii)

20

m
(iv)

10

√

2

m
(v)

5

√

12

m

Assignment Key